We study field models for which a quantum action (i.e. the action appearing in the generating functional of Green functions) is invariant under supersymmetric transformations. We derive the Ward identity which is direct consequence of this invariance
. We consider a change of variables in functional integral connected with supersymmetric transformations when its parameter is replaced by a nilpotent functional of fields. Exact form of the corresponding Jacobian is found. We find restrictions on generators of supersymmetric transformations when a consistent quantum description of given field theories exists.
